Mathematics is as much a part of our humanity as music and art. And it is our mathematics that might be understandable, even familiar, to a distant race and might provide the basis for mutual communication. This book discusses, in a conversational way, the role of mathematics in the search for extraterrestrial intelligence. The author explores the science behind that search, its history, and the many questions associated with it, including those regarding the nature of language and the philosophical/psychological motivation behind this search.
Discover how mathematical sequences abound in our natural world in this definitive exploration of the geography of the cosmos You need not be a philosopher or a botanist, and certainly not a mathematician, to enjoy the bounty of the world around us. But is there some sort of order, a pattern, to the things that we see in the sky, on the ground, at the beach? In A Beginner's Guide to Constructing the Universe, Michael Schneider, an education writer and computer consultant, combines science, philosophy, art, and common sense to reaffirm what the ancients observed: that a consistent language of geometric design underpins every level of the universe, from atoms to galaxies, cucumbers to cathedrals. Schneider also discusses numerical and geometric symbolism through the ages, and concepts such as periodic renewal and resonance. This book is an education in the world and everything we can't see within it. Contains numerous b&w photos and illustrations.
This work presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.
An innovative treatment of mathematical methods for a multidisciplinary audience Clearly and elegantly presented, Mathematical Methods in Science and Engineering provides a coherent treatment of mathematical methods, bringing advanced mathematical tools to a multidisciplinary audience. The growing interest in interdisciplinary studies has brought scientists from many disciplines such as physics, mathematics, chemistry, biology, economics, and finance together, which has increased the demand for courses in upper-level mathematical techniques. This book succeeds in not only being tuned in to the existing practical needs of this multidisciplinary audience, but also plays a role in the development of new interdisciplinary science by introducing new techniques to students and researchers. Mathematical Methods in Science and Engineering's modular structure affords instructors enough flexibility to use this book for several different advanced undergraduate and graduate level courses. Each chapter serves as a review of its subject and can be read independently, thus it also serves as a valuable reference and refresher for scientists and beginning researchers. There are a growing number of research areas in applied sciences, such as earthquakes, rupture, financial markets, and crashes, that employ the techniques of fractional calculus and path integrals. The book's two unique chapters on these subjects, written in a style that makes these advanced techniques accessible to a multidisciplinary audience, are an indispensable tool for researchers and instructors who want to add something new to their compulsory courses. Mathematical Methods in Science and Engineering includes: * Comprehensive chapters on coordinates and tensors and on continuous groups and their representations * An emphasis on physical motivation and the multidisciplinary nature of the methods discussed * A coherent treatment of carefully selected topics in a style that makes advanced mathematical tools accessible to a multidisciplinary audience * Exercises at the end of every chapter and plentiful examples throughout the book Mathematical Methods in Science and Engineering is not only appropriate as a text for advanced undergraduate and graduate physics programs, but is also appropriate for engineering science and mechanical engineering departments due to its unique chapter coverage and easily accessible style. Readers are expected to be familiar with topics typically covered in the first three years of science and engineering undergraduate programs. Thoroughly class-tested, this book has been used in classes by more than 1,000 students over the past eighteen years.
Rewarding undergraduate text, derived from an experimental program in teaching mathematics at the secondary-school level. This text provides a good introduction to geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. "...solid modern mathematical content..." — American Scientist. Over 200 figures. 1964 edition.
The term used in the title of this volume--thinking practices--evokes questions that the authors of the chapters within it begin to answer: What are thinking practices? What would schools and other learning settings look like if they were organized for the learning of thinking practices? Are thinking practices general, or do they differ by disciplines? If there are differences, what implications do those differences have for how we organize teaching and learning? How do perspectives on learning, cognition, and culture affect the kinds of learning experiences children and adults have? This volume describes advances that have been made toward answering these questions. These advances involve several agendas, including increasing interdisciplinary communication and collaboration; reconciling research on cognition with research on teaching, learning, and school culture; and strengthening the connections between research and school practice. The term thinking practices is symbolic of a combination of theoretical perspectives that have contributed to the volume editors' understanding of how people learn, how they organize their thinking inside and across disciplines, and how school learning might be better organized. By touring through some of the perspectives on thinking and learning that have evolved into school learning designs, Greeno and Goldman begin to establish a frame for what they are calling thinking practices. This volume is a significant contribution to a topic that they believe will continue to emerge as a coherent body of scientific and educational research and practice.
Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This volume, originally published in 1959, contains the first sixteen columns published in the magazine from 1956-1958. They were reviewed and briefly updated by Gardner for this 1988 edition.
Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. In her book, she offers you the tools needed to get a better grasp of that intimidating but inescapable field.
This book offers an engaging and comprehensive introduction to scientific theories and the evolution of science and mathematics through the centuries. It discusses the history of scientific thought and ideas and the intricate dynamic between new scientific discoveries, scientists, culture and societies. Through stories and historical accounts, the volume illustrates the human engagement and preoccupation with science and the interpretation of natural phenomena. It highlights key scientific breakthroughs from the ancient to later ages, giving us accounts of the work of ancient Greek and Indian mathematicians and astronomers, as well as of the work of modern scientists like Descartes, Newton, Planck, Mendel and many more. The author also discusses the vast advancements which have been made in the exploration of space, matter and genetics and their relevance in the advancement of the scientific tradition. He provides great insights into the process of scientific experimentation and the relationship between science and mathematics. He also shares amusing anecdotes of scientists and their interactions with the world around them. Detailed and accessible, this book will be of great interest to students and researchers of science, mathematics, the philosophy of science, science and technology studies and history. It will also be useful for general readers who are interested in the history of scientific discoveries and ideas.
Successful game programming requires at least a rudimentary understanding of central math topics. While most books neglect the point-by-point details that are necessary to truly hone these skills, Beginning Pre-Calculus for Game Developers tackles each task head on, using easy-to-understand, hands-on exercises. You will conquer the basics of these essential math topics and will then learn how to specifically apply each skill to the field of game programming. Whether you are searching for an entertaining, engaging way to improve your math skills or you wish to develop the background skills necessary to boost your game programming, Beginning Pre-Calculus for Game Developers serves as the step-by-step guide that will help you tackle pre-calculus with confidence.
